Definition 1

Tag 0035, permanent. Cite it as [Bourbaki, Tag 0035].

Algebra, VIII, p. 45, § 3. Simple Modules

Let A be a ring. An A-module M is called simple if it is nonzero and has no submodule distinct from 0 and M.

An A-module M is simple if and only if M is a simple module over its ring of homotheties $A_M$ . Every simple module is indecomposable, of length 1, and therefore primordial (VIII, p. 31, Proposition 4, b)).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Definition 2, Appendix 1

Cites

VIII, p. 31, Proposition 4